Around the Joint Behavior of Independent Random Tensor Matrices - Lecture 1
Explore joint behavior of independent random tensor matrices with smaller symmetry groups. Learn about tensor structures, generalizations of free probability, and new analytical techniques.
Higher Rank Voronoi Decompositions and Metric Degenerations of Tori
Explore higher rank Voronoi decompositions and their applications in studying asymptotic geometry of Riemann surfaces and moduli spaces.
Tropicalization of the Universal Jacobian: Logarithmic and Non-Archimedean Views
Explore tropicalization of universal Jacobians, examining logarithmic and non-archimedean perspectives. Gain insights into moduli spaces, cone stacks, and new stability conditions for compactified Jacobians.
Spectral Theory of Stationary Spacetimes - Part I
Explore spectral theory in stationary spacetimes, delving into mathematical concepts at the intersection of relativity and quantum mechanics.
Initial Data Rigidity via Dirac-Witten Operators
Explore initial data rigidity in spin settings using Dirac-Witten operators. Derive a rigidity theorem for manifolds with boundary, examining dominant energy conditions and null expansion scalars.
Nonlinear Hyperbolic Conservation Laws on Manifolds
Explore nonlinear scalar hyperbolic equations on Riemannian varieties, covering existence, uniqueness, entropy conditions, finite-volume schemes, and numerical results.
Continuum Limits for Discrete Dirac Operators on 2D Square Lattices
Explore continuum limits of discrete Dirac operators on 2D square lattices, focusing on convergence in strong resolvent sense and implications for complex analysis and quantum theory.
Geometrically Induced Discrete Eigenvalues of Dirac Operators with Lorentz Scalar Delta-Shell Interactions
Explore geometrically induced discrete eigenvalues of Dirac operators with Lorentz scalar δ-shell interactions on broken lines, revealing novel spectral properties in quantum theory.
Schrödinger Operators with Oblique Transmission Conditions in R2
Explore Schrödinger operators with oblique transmission conditions, examining self-adjointness, spectral properties, and connections to Dirac operators with delta-potentials in quantum theory.
A New Approach to the Hot Spots Conjecture
Explore a novel approach to the hot spots conjecture in mathematics, focusing on eigenvalues of Neumann and Dirichlet Laplacians and recent advances in the field.
On the Rearrangement of a Function and Its Applications
Explore classical results and applications of function rearrangement, including recent developments in shape and topology optimization.
Schoen's Conjecture for Limits of Isoperimetric Surfaces
Explore Schoen's conjecture for asymptotically flat Riemannian manifolds, focusing on area-minimizing hypersurfaces and recent developments in mathematical relativity.
Oka Tubes in Holomorphic Line Bundles
Explore Oka tubes in holomorphic line bundles with Franc Forstneric, delving into advanced concepts in complex analysis and geometry.
Rational Sphere Maps: Symmetries, Gaps, and Optimization
Explore rational sphere maps, analyzing symmetries, gaps, and optimization in complex variables. Gain insights into target dimensions, equivariant groups, and the Whitney map.
Globally Hyperbolic Anti-de Sitter Manifolds and Compact Clifford-Klein Forms
Explore globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms in advanced geometry, focusing on curvature and rigidity concepts.
Schmutz-Thurston Duality in Mapping Class Group-Equivariant Cell Decompositions
Explore mapping class group-equivariant cell decompositions of Teichmueller space, focusing on Schmutz and Thurston's work for closed compact surfaces without marked points.
A Unified Approach to Extremal Curves on Stiefel Manifolds
Explore extremal curves on Stiefel manifolds through a unified framework, examining Euler-Lagrange equations and their applications in applied mathematics.
Harmonic Maps and Random Walks on Countable Groups
Explore harmonic maps and random walks on countable groups, focusing on CAT(0) spaces and group actions with zero escape rate.
Rational Maps of Bruhat-Tits Buildings
Explore "rational" maps of Bruhat-Tits buildings in this advanced mathematics lecture by Yurii Neretin, delving into geometric structures and their transformations.
The Funk Metric in Convex Geometry and Related Fields
Explore the Funk metric's connections to convex geometry, affine geometry, and combinatorics. Discover its projective invariance and relations to various conjectures and theorems.
Group Representations on 2D Topological Quantum Field Theories
Explore group representations in 2D topological quantum field theories, delving into advanced mathematical concepts and their applications in theoretical physics.